Dynamic Gaussian Processes and the Vanilla-SPDE Exchange
For researchers and practitioners using Gaussian processes for spatio-temporal modeling, this work offers a computationally cheaper hybrid inference scheme.
The paper tackles the cubic computational cost of Gaussian process inference in spatio-temporal settings, proposing the Vanilla-SPDE Exchange that reduces complexity by exploiting an equivalence between standard and SPDE formulations. Numerical experiments confirm improved computational efficiency.
Gaussian process inference is often limited by cubic computational costs, a challenge that becomes more pronounced in spatio-temporal settings where posterior inference is required over dense grids. While state-space SPDE formulations enable linear complexity in time, exact inference remains cubic in space and deteriorates further when observation locations are disjoint from the prediction locations, which inflates the number of considered spatial points. To address this, we propose the Vanilla-SPDE Exchange, which exploits an equivalence between the standard and SPDE formulations of GP inference to construct a hybrid scheme with improved computational cost. We demonstrate these gains through complexity analysis and numerical experiments.